In the following figure, four curves $A, B, C$ and $D$ are shown. The curves are

One mole of an ideal gas expands adiabatically from an initial state $\left(T_A, V_0\right)$ to final state $\left(T_f, 5 V_0\right)$. Another mole of the same gas expands isothermally from a different initial state ( $T_{\mathrm{B}}, \mathrm{V}_0$ ) to the same final state $\left(T_{\mathrm{f}}, 5 V_0\right)$. The ratio of the specific heats at constant pressure and constant volume of this ideal gas is $\gamma$. What is the ratio $T_{\mathrm{A}} / T_{\mathrm{B}}$ ?

If $\gamma $ denotes the ratio of two specific heats of a gas, the ratio of slopes of adiabatic and isothermal $PV$ curves at their point of intersection is

An adiabatic process occurs at constant

An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the figure). Initially the gas is at temperature $T _1$, pressure $P_1$ and volume $V_1$ and the spring is in its relaxed state. The gas is then heated very slowly to temperature $T_2$, pressure $P _2$ and volume $V _2$. During this process the piston moves out by a distance $x$. Ignoring the friction between the piston and the cylinder, the correct statement$(s)$ is(are)

$(A)$ If $V_2=2 V_1$ and $T_2=3 T_1$, then the energy stored in the spring is $\frac{1}{4} P_1 V_1$

$(B)$ If $V_2=2 V_1$ and $T_2=3 T_1$, then the change in internal energy is $3 P_1 V_1$

$(C)$ If $V_2=3 V_1$ and $T_2=4 T_1$, then the work done by the gas is $\frac{7}{3} P_1 V_1$

$(D)$ If $V_2=3 V_1$ and $T_2=4 T_1$, then the heat supplied to the gas is $\frac{17}{6} P_1 V_1$